Tiger Woods' airbags didn't deploy in his recent accident, reportedly because the vehicle was going slower than 33 mph.
Check your owner's manual. A CarSpace member says that this language is in some GM manuals:
"In any particular crash, no one can say whether an airbag should have inflated simply because of the damage to the vehicle or because of what the repair costs were. For frontal airbags, inflation is determined by what the vehicle hits, the angle of the impact, and how quickly the vehicle slows down. For roof-rail airbags, deployment is determined by the location and severity of the side impact."
You generally don't want the airbags going off in low speed or low impact crashes because the injuries that can be caused by the airbags can be worse than those caused by the wreck itself.